{ "schemaVersion": 1, "generatedAt": "2026-11-10T14:17:21.943434+00:00", "protocol": { "version": "calibration-rating-uncertainty-v2", "declaredBeforeVariantScoring": "2026-11-10", "parent": "strength-bracket-v1", "temperatureBounds": [ 0.5, 3.0 ], "logTemperaturePriorSd": 0.5, "ratingDraws": 1024, "ratingSeed": 1973, "featureExperiment": "14 predeclared retrained variants: strength, home, record, seed, recent-20 residual; raw margin comparator", "notes": [ "Designed after inspecting v1. Reusing its 31 seasons is exploratory comparison, not a fresh holdout.", "Temperature uses only earlier forward forecasts, including 1990-1994 warm-up predictions; target outcomes never fit their own calibration.", "MAP log-temperature prior is N(0, 0.5^2), bounded to temperatures 0.5-3. No further hyperparameter search.", "Uncertainty integrates a correlated empirical-Bayes Gaussian rating approximation through the complete bracket, holding the v1 game link fixed.", "80/95 percent rating-conditional intervals omit coefficient, calibration, injury, roster and model misspecification uncertainty. They have no established coverage for true title probabilities.", "All v1 inputs, eligible fields, C selection and evaluation seasons are preserved. No current market trading or staking policy is evaluated." ] }, "methodology": { "calibration": "Temperature scaling: q_i = p_i^(1/T) / sum_j p_j^(1/T). T is fitted to earlier forward-season forecasts only, with a prior toward 1; no target outcome participates. Calibration changes confidence, not ranking.", "uncertainty": "Empirical-Bayes Gaussian rating uncertainty from regular-season residuals and ridge covariance. One correlated strength vector persists through every postseason game. 1,024 scrambled Sobol draws integrate exact conditional brackets.", "limitations": [ "Designed after inspecting v1. Reusing its 31 seasons is exploratory comparison, not a fresh holdout.", "Temperature uses only earlier forward forecasts, including 1990-1994 warm-up predictions; target outcomes never fit their own calibration.", "MAP log-temperature prior is N(0, 0.5^2), bounded to temperatures 0.5-3. No further hyperparameter search.", "Uncertainty integrates a correlated empirical-Bayes Gaussian rating approximation through the complete bracket, holding the v1 game link fixed.", "80/95 percent rating-conditional intervals omit coefficient, calibration, injury, roster and model misspecification uncertainty. They have no established coverage for true title probabilities.", "All v1 inputs, eligible fields, C selection and evaluation seasons are preserved. No current market trading or staking policy is evaluated.", "Intervals apply only to the uncalibrated uncertainty model. They are conditional model bands, not a validated bound on the true probability or a safe staking rule.", "No historical executable prices, slippage, fees or portfolio drawdowns have been backtested. This experiment cannot establish trading profitability." ] }, "coverage": { "firstSeason": 1985, "lastSeason": 2026, "evaluatedSeasons": 31, "gameCount": 51507, "phaseCounts": { "regular": 48174, "playoff": 3296, "play_in": 37 }, "excludedSeasons": [ { "season": 2020, "reason": "Bubble neutral sites and asymmetric 8/9 qualification need their own format model." } ] }, "models": [ { "id": "uniform", "name": "Equal chances", "description": "Every eligible team has the same title probability: 1/16 historically, 1/20 in play-in seasons.", "metrics": { "logLoss": 2.815777796687694, "brier": 0.9399193548387096, "topPickAccuracy": 0.06008064516129033 } }, { "id": "seed_history", "name": "Historical seeds", "description": "Earlier champions' conference seed frequencies, with 0.5 pseudocount per rank, normalized across the current field.", "metrics": { "logLoss": 2.0007236726035917, "brier": 0.823611660728316, "topPickAccuracy": 0.27419354838709675 } }, { "id": "record_bracket", "name": "Record + bracket", "description": "Same trained game model and exact bracket, using regular-season win percentage instead of adjusted scoring margin.", "metrics": { "logLoss": 1.831947169451371, "brier": 0.7501185365992354, "topPickAccuracy": 0.41935483870967744 } }, { "id": "strength_bracket", "name": "Strength + bracket", "description": "Opponent-adjusted regular-season scoring margin, a game model fitted only on earlier playoffs, and exact bracket probabilities.", "metrics": { "logLoss": 1.7592187116812261, "brier": 0.7265999360519623, "topPickAccuracy": 0.3870967741935484 } }, { "id": "calibrated_strength", "name": "Strength + calibration", "description": "One title-level temperature fitted only on earlier forward forecasts; preserves team ranking.", "metrics": { "logLoss": 1.7870762485470626, "brier": 0.7386672202998099, "topPickAccuracy": 0.3870967741935484 } }, { "id": "uncertain_strength", "name": "Strength + uncertainty", "description": "Average exact brackets over 1,024 correlated 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Training-only RMS scaling; no free intercept; signed home indicator is unscaled.", "recentForm": "Mean scoring-margin residual in each team's last 20 regular games, after subtracting the full-season adjusted strength difference and estimated home effect.", "seed": "Negative conference seed before 2020; negative regular-season conference rank before play-in from 2021. Bracket positions remain fixed across variants, including variants omitting seed as a game-model feature.", "scoring": "Title metrics are averaged equally across seasons. Game metrics first average playoff games within each season, then average seasons equally; every game uses frozen regular-season-end features, including later rounds.", "interpretation": "A positive drop-one-minus-full loss difference means removing that feature hurt the full model. Contributions are conditional on the other correlated features and are not causal effects. Addition-minus-v1 differences favor the addition when negative." }, "limitations": [ "Fourteen prespecified comparisons reuse already-inspected historical seasons; these are exploratory follow-up results, not a fresh untouched holdout. Confidence intervals are descriptive and not multiplicity-adjusted.", "Only score-derived signals are tested. Possession-adjusted offense/defense, shooting, turnovers, injuries, players, and market prices cannot be ranked from these inputs.", "Strength, record, and seed are strongly related. A small drop-one effect does not show that a feature lacks standalone information.", "Home-court ablation removes the learned venue effect but retains actual seeding, bracket structure, and regular-season home correction used to estimate strength.", "Raw margin versus adjusted strength compares the full rating construction, including home/schedule adjustment and fixed shrinkage, rather than isolating schedule adjustment alone.", "The same regular-season-end cutoff and exclusion of 2020 apply to every variant. No target postseason scores are feature inputs." ], "audit": { "v1ParityVerified": true, "inputHashes": { "games.csv": "8e379c60fa38ae25d64d3fc3d10505a0d9856cd18e3dd3b99ae87984623f4275", "seedings.json": "3c832326d74b53e15f98d6e6dcf33594d86037b0c55b0846b37acbaf087fe7b2" }, "featureModuleHash": "01f12f54fec3a2aa23771b29fe71d2f3b990570cbf0e345479008939f5f837c1", "protocolHash": "3413ee17e39b32dbc44236962e691e23a561b79e0fb452702a260571e2d5b114" } }, "audit": { "frozenV1Hash": "cbd0972f0cd6b1e8cfa448f73c158d69aced5e23c16359ba9be0897ea59f98b8", "protocolHash": "7745de9843aabc1961759986c1cb0198eaaea9b23a3a1c525dfe2e9634be68a6", "inputHashes": { "games.csv": "8e379c60fa38ae25d64d3fc3d10505a0d9856cd18e3dd3b99ae87984623f4275", "seedings.json": "3c832326d74b53e15f98d6e6dcf33594d86037b0c55b0846b37acbaf087fe7b2" }, "calibration": [ { "season": 1990, "temperature": { "temperature": 1.0, "through": null, "seasons": 0 }, "uncertainTemperature": { "temperature": 1.0, "through": null, "seasons": 0 }, 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"ESPN dated scoreboards", "url": "https://site.api.espn.com/apis/site/v2/sports/basketball/nba/scoreboard" }, { "title": "NBA first-round format changed in 2003", "url": "https://www.nba.com/news/history-season-review-2002-03" }, { "title": "Bucks media guide: Finals tiebreak changed in 1991 (page 260)", "url": "https://nyc3.digitaloceanspaces.com/sportsarchive-documents/prod/698bdc3c08deb/2008_Media_Guide.pdf#page=260" }, { "title": "Temperature scaling methodology (Guo et al., 2017)", "url": "https://proceedings.mlr.press/v70/guo17a.html" } ] }